A195016 a(n) = (n*(5*n+7) - (-1)^n + 1)/2.

0, 7, 17, 34, 54, 81, 111, 148, 188, 235, 285, 342, 402, 469, 539, 616, 696, 783, 873, 970, 1070, 1177, 1287, 1404, 1524, 1651, 1781, 1918, 2058, 2205, 2355, 2512, 2672, 2839, 3009, 3186, 3366, 3553, 3743, 3940, 4140, 4347, 4557, 4774, 4994, 5221, 5451, 5688

Offset

0,2

Comments

Sequence found by reading the line from 0, in the direction 0, 7,..., and the same line from 0, in the direction 0, 17,..., in the square spiral whose edges have length A195013 and whose vertices are the numbers A195014. Axis perpendicular to the main axis A195015 in the same spiral.

Also sequence found by reading the line from 0, in the direction 0, 7,..., and the same line from 0, in the direction 0, 17,..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. This line is parallel to A153126 in the same spiral.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

n*(10*n-3), if n >= 1, and (2*n+1)*(5*n+1) - 1, if n >= 0, interleaved.

G.f.: x*(7+3*x)/((1+x)*(1-x)^3). - Bruno Berselli, Oct 14 2011

From Elmo R. Oliveira, Jun 19 2026: (Start)

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).

E.g.f.: (x*(5*x + 12)*cosh(x) + (5*x^2 + 12*x + 2)*sinh(x))/2. (End)

Mathematica

LinearRecurrence[{2, 0, -2, 1}, {0, 7, 17, 34}, 50] (* Paolo Xausa, Feb 09 2024 *)

Prog

(Magma) &cat[[n*t, (n+1)*t] where t is 10*n+7: n in [0..22]]; // Bruno Berselli, Oct 14 2011

Crossrefs

Cf. A000566, A005476, A028895, A033571, A085787, A152965, A153126, A195013, A195014, A195015.

Sequence in context: A278920 A074275 A051411 * A296553 A101121 A212117

Adjacent sequences: A195013 A195014 A195015 * A195017 A195018 A195019

Keyword

nonn,easy

Author

Omar E. Pol, Sep 26 2011

Extensions

Concise definition by Bruno Berselli, Oct 14 2011

Status

approved