A093918 a(2k-1)=(2k-1)^2+k, a(2k)=6k^2+k+1: Last term in rows of triangle A093915.

2, 8, 11, 27, 28, 58, 53, 101, 86, 156, 127, 223, 176, 302, 233, 393, 298, 496, 371, 611, 452, 738, 541, 877, 638, 1028, 743, 1191, 856, 1366, 977, 1553, 1106, 1752, 1243, 1963, 1388, 2186, 1541, 2421, 1702, 2668, 1871, 2927, 2048, 3198, 2233, 3481, 2426, 3776

Offset: 1

Author

Amarnath Murthy, Apr 25 2004

Keywords

• nonn
• easy

Comments

Initially defined as "leading diagonal" of the triangle A093915, a(n) is the last term in row n of A093915, i.e. a(n)=A093916(n)+n-1. - M. F. Hasler, Apr 04 2009

Links

• Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

Crossrefs

Cf. A093915, A093916, A093917.

Programs

Mathematica

LinearRecurrence[{0,3,0,-3,0,1},{2,8,11,27,28,58},50] (* Harvey P. Dale, Oct 22 2013 *)

PARI

A093918(n)=if(n%2,n^2,6*(n\2)^2)+n\2+1 \\ M. F. Hasler, Apr 04 2009

Formula

Equals A093915 o A000217 = A093916 + A023443. - M. F. Hasler, Apr 04 2009

a(n) = (3+(-1)^n+2*n+(5+(-1)^n)*n^2)/4. a(n) = 3*a(n-2)-3*a(n-4)+a(n-6). G.f.: -x*(x^2+2*x+2)*(x^3-x^2+3*x+1) / ((x-1)^3*(x+1)^3). - Colin Barker, Dec 18 2012

Extensions

Edited and extended beyond a(6) by M. F. Hasler, Apr 04 2009