Triangular number 12

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The Christmas song "The twelve days of Christmas", in the final verse, has 12 lines, or parts, and 78 gifts. The number 78 is an example of a "triangular number". The song is sung over and over.

How many total gifts?

364 plus the baby Jesus

The verses keep adding another line, so the song can be quite long when sung in entirety. How many gifts total?

1*12 + 2*11 + 3*10 + 4*9 + 5*8 + 6*7 + 7*6 + 8*5 + 9*4 + 10*3 + 11*2 12*1

If one adds all the triangular numbers from 1 to 12, when singing all twelve verses, the total number of gifts is 364. In mathematical terms, the number of gifts g is given by the following formula.

$Gift total for the twelve days of Christmas$
According to some Christian traditions, the last gift, to make a gift for each day of the year (ignoring leap years), is the gift on Christmas of the birth of the baby Jesus.

Of course, computer scientists or software engineers may prefer to use a program to count the gifts, such is in the following Lua program.

Here is the Lua code [#1]

local g = 0
for v=1,12 do
	for i=v,1,-1 do
		g = g + i
		end
	end
print(string.format("g(12) = %d",g))

Here is the output of the Lua code.

g(12) = 364

The Portuguese word "lua" ≈ "moon". Lua was developed in Brazil and has a syntax based on the Pascal (and Modula-2) programming languages.

Here is a list of "gift" numbers for verses from 1 to 30 in the sense of the total gifts in the "12 days of Christmas". Here is a Lua program to compute these value.

Here is the Lua code [#2]

for n=1,30 do
	local g = 0
	for v=1,n do
		for i=v,1,-1 do
			g = g + i
			end
		end
	print(string.format("g(%d) = %d",n,g))
	end

Here is the output of the Lua code.

g(1) = 1
g(2) = 4
g(3) = 10
g(4) = 20
g(5) = 35
g(6) = 56
g(7) = 84
g(8) = 120
g(9) = 165
g(10) = 220
g(11) = 286
g(12) = 364
g(13) = 455
g(14) = 560
g(15) = 680
g(16) = 816
g(17) = 969
g(18) = 1140
g(19) = 1330
g(20) = 1540
g(21) = 1771
g(22) = 2024
g(23) = 2300
g(24) = 2600
g(25) = 2925
g(26) = 3276
g(27) = 3654
g(28) = 4060
g(29) = 4495
g(30) = 4960

The Portuguese word "lua" ≈ "moon". Lua was developed in Brazil and has a syntax based on the Pascal (and Modula-2) programming languages.