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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 (list; graph; refs; listen; history; text; internal format)
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+1-n)/2], Floor[(i+1-n)/2]+n-Mod[i-n, 2]}], {i, n, 3n}]; Array[a, 21, 0] (* Stefano Spezia, Jan 21 2024 *)
CROSSREFS
Sequence in context: A192903 A050793 A281203 * A126633 A125422 A190988
KEYWORD
nonn
AUTHOR
Nicolay Avilov, Jan 20 2024
EXTENSIONS
a(6)-a(20) from Alois P. Heinz, Jan 20 2024
STATUS
approved

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Last modified May 18 16:58 EDT 2024. Contains 372664 sequences. (Running on oeis4.)