A131228 -id:A131228 - cp's OEIS frontend

A131229 Numbers congruent to {1,7} mod 10.

1, 7, 11, 17, 21, 27, 31, 37, 41, 47, 51, 57, 61, 67, 71, 77, 81, 87, 91, 97, 101, 107, 111, 117, 121, 127, 131, 137, 141, 147, 151, 157, 161, 167, 171, 177, 181, 187, 191, 197, 201, 207, 211, 217, 221, 227, 231, 237, 241, 247, 251, 257, 261, 267, 271, 277, 281

Offset: 1

Gary W. Adamson, Jun 20 2007

Row sums of triangle A131228.
Take the sum of the squares of the first n triangular numbers and divide it by the sum of these n triangular numbers.  The sum evenly divides the sum of the squares for the n in this sequence. - J. M. Bergot, May 09 2012
a(n) = the difference between the sum of the terms in antidiagonal(n) and antidiagonal(n-1) in A204008. - J. M. Bergot, Jul 15 2013

			11 = a(3) = 1 mod 10.
11 = a(3) = row 4 sums, triangle A131228: (1 + 3 + 7).

David Lovler, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A001622, A128174, A051340, A063097, A131228.

Select[Range[300],MemberQ[{1,7},Mod[#,10]]&] (* or *) LinearRecurrence[ {1,1,-1},{1,7,11},60] (* Harvey P. Dale, May 20 2012 *)

is(n)=n%10==1 || n%10==7 \\ Charles R Greathouse IV, Jul 16 2013

From R. J. Mathar, Apr 17 2008: (Start)
a(n) = a(n-2) + 10 = 5*n + ((-1)^n - 7)/2.
G.f.: x*(1 + 6*x + 3*x^2)/((-1+x)^2*(1+x)). (End)
a(n) = 10*n - a(n-1) - 12 with n > 1, a(1)=1. - Vincenzo Librandi, Nov 23 2010
a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3; a(1)=1, a(2)=7, a(3)=11. - Harvey P. Dale, May 20 2012
a(n) = A063097(n) for n >= 2. - Georg Fischer, Nov 02 2018
E.g.f.: 3 + ((10*x - 7)*exp(x) + exp(-x))/2. - David Lovler, Sep 07 2022
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt((5+sqrt(5))/2)*Pi/10 + 3*log(phi)/(2*sqrt(5)), where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023

More terms from R. J. Mathar, Apr 17 2008

A131227 2*A051340 - A128174.

Original entry on oeis.org

1, 2, 3, 1, 2, 5, 2, 1, 2, 7, 1, 2, 1, 2, 9, 2, 1, 2, 1, 2, 11, 1, 2, 1, 2, 1, 2, 13, 2, 1, 2, 1, 2, 1, 2, 15, 1, 2, 1, 2, 1, 2, 1, 2, 17, 2, 1, 2, 1, 2, 1, 2, 1, 2, 19

Offset: 0

Gary W. Adamson, Jun 20 2007

Row sums = A047383, numbers congruent to {1,5} mod 7: (1, 5, 8, 12, 15, 19, ...)

			First few rows of the triangle:
  1;
  2, 3;
  1, 2, 5;
  2, 1, 2, 7;
  1, 2, 1, 2, 9;
  2, 1, 2, 1, 2, 11;
  1, 2, 1, 2, 1,  2, 13;
  ...

Cf. A051340, A128174, A047383, A131228, A131229.

2*A051340 - A128174 as infinite lower triangular matrices.

cp's OEIS Frontend

A131229 Numbers congruent to {1,7} mod 10.

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