A131844 -id:A131844 - cp's OEIS frontend

A131873 Right-to-left partial row sums of triangle A131844.

1, 8, 4, 15, 8, 7, 22, 12, 11, 10, 29, 16, 15, 14, 13, 36, 20, 19, 18, 17, 16, 43, 24, 23, 22, 21, 20, 19, 50, 28, 27, 26, 25, 24, 23, 22, 57, 32, 31, 30, 29, 28, 27, 26, 25, 64, 36, 35, 34, 33, 32, 31, 30, 29, 28, 71, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 78, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 85, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 92, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40

Offset: 0

Gary W. Adamson, Jul 22 2007

Left column = A016993, 7n + 1: (1, 8, 15, 22, 29, ...).
Right border = 3n + 1: (1, 4, 7, 10, 13, ...).
Row sums = A131874: (1, 12, 30, 55, ...).

			First few rows of the triangle:
   1;
   8,  4;
  15,  8,  7;
  22, 12, 11, 10;
  29, 16, 15, 14, 13;
  36, 20, 19, 18, 17, 16;
  43, 24, 23, 22, 21, 20, 19;
  ...
Row 4 of A131844 is 13, 1, 1, 1, 13, so row 4 of this sequence is 29, 16, 15, 14, 13.

Cf. A131844, A131874, A016993, A131875.

Definition corrected and more terms added by Russ Cox, Apr 18 2024

A131875 Triangle, A000012 * A131844 as infinite lower triangular matrices.

Original entry on oeis.org

1, 5, 4, 12, 5, 7, 22, 6, 8, 10, 35, 7, 9, 11, 13, 51, 8, 10, 12, 14, 16, 70, 9, 11, 13, 15, 17, 19, 92, 10, 12, 14, 16, 18, 20, 22, 117, 11, 13, 15, 17, 19, 21, 23, 25, 145, 12, 14, 16, 18, 20, 22, 24, 26, 28

Offset: 0

Gary W. Adamson, Jul 22 2007

Left column = pentagonal numbers, A000326: (1, 5, 12, 22, ...).

Row sums = A001106: (1, 9, 24, 46, 75, 111, ...).

			First few rows of the triangle:
   1;
   5,  4;
  12,  5,  7;
  22,  6,  8, 10;
  35,  7,  9, 11, 13;
  51,  8, 10, 12, 14, 16;
  70,  9, 11, 13, 15, 17, 19;
  92, 10, 12, 14, 16, 18, 20, 22;
  ...

Cf. A131844, A001106, A000326.

A016993 a(n) = 7*n + 1.

Original entry on oeis.org

1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85, 92, 99, 106, 113, 120, 127, 134, 141, 148, 155, 162, 169, 176, 183, 190, 197, 204, 211, 218, 225, 232, 239, 246, 253, 260, 267, 274, 281, 288, 295, 302, 309, 316, 323, 330, 337, 344, 351, 358, 365, 372, 379

Offset: 0

N. J. A. Sloane

For n > 3, also the number of (not necessarily maximal) cliques in the n-web graph. - Eric W. Weisstein, Nov 29 2017

The number of notes in a musical scale of n octaves. - Geoffrey Trueman Falk, Feb 16 2023

Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Tanya Khovanova, Recursive Sequences
Eric Weisstein's World of Mathematics, Clique
Eric Weisstein's World of Mathematics, Web Graph
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A093564 (column 1).

Cf. A131844, A008589.

a016993 = (+ 1) . (* 7)
a016993_list = [1, 8 ..]  -- Reinhard Zumkeller, Jan 25 2013

[7*n+1: n in [0..60]]; // Vincenzo Librandi, May 28 2011

A016993:=n->7*n+1: seq(A016993(n), n=0..70); # Wesley Ivan Hurt, Nov 01 2014

7*Range[0, 55] + 1 (* Alonso del Arte, Oct 26 2014 *)
Table[7 n + 1, {n, 0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
LinearRecurrence[{2, -1}, {8, 15}, {0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
CoefficientList[Series[(1 + 6 x)/(-1 + x)^2, {x, 0, 20}], x] (* Eric W. Weisstein, Nov 29 2017 *)

a(n)=7*n+1 \\ Charles R Greathouse IV, Jul 10 2016

a(n) = 7*n + 1.
G.f.: (1+6*x)/(1-x)^2.
From Elmo R. Oliveira, Mar 07 2024: (Start)
a(n) = 2*a(n-1) - a(n-2).
E.g.f.: (1 + 7*x)*exp(x). (End)

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A131873 Right-to-left partial row sums of triangle A131844.

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A131875 Triangle, A000012 * A131844 as infinite lower triangular matrices.

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A016993 a(n) = 7*n + 1.

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