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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 Alois P. Heinz, Table of n, a(n) for n = 0..1106 Nicolay Avilov, Illustration for terms a(0) - a(4). 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 Cf. A007318, A030662. Sequence in context: A192903 A050793 A281203 * A126633 A125422 A190988 Adjacent sequences: A369332 A369333 A369334 * A369336 A369337 A369338 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.)