

A369335


a(n) is the sum of the numbers inside a square of side length 2n+1 located in Pascal's triangle at and below row n.


1



1, 10, 94, 816, 6872, 57038, 469238, 3836430, 31221874, 253198806, 2047761014, 16526046182, 133145419056, 1071276327274, 8610169465642, 69143029079432, 554860626424744, 4450160058135914, 35675446422203960, 285892025190834636, 2290356743575612582
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OFFSET

0,2


COMMENTS

We will assume that the numbers of Pascal's triangle are written in the cells of a square lattice. Then row n has width 2n+1 and the square of cells starts there.


LINKS



FORMULA

Limit_{n>oo} a(n+1)/a(n) = 8.


EXAMPLE

a(0) = 1.
a(1) = 1 + 1 + 2 + 3 + 3 = 10.

 1 2 1 
 3 3 
a(2) = Sum  4 6 4  = 94.
 10 10 
 15 20 15



MATHEMATICA

a[n_]:=Sum[Sum[Binomial[i, k], {k, Floor[(i+1n)/2], Floor[(i+1n)/2]+nMod[in, 2]}], {i, n, 3n}]; Array[a, 21, 0] (* Stefano Spezia, Jan 21 2024 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



