A143690 a(n) = A007318 * [1, 6, 14, 9, 0, 0, 0, ...].

1, 7, 27, 70, 145, 261, 427, 652, 945, 1315, 1771, 2322, 2977, 3745, 4635, 5656, 6817, 8127, 9595, 11230, 13041, 15037, 17227, 19620, 22225, 25051, 28107, 31402, 34945, 38745, 42811, 47152, 51777, 56695, 61915, 67446, 73297, 79477, 85995, 92860, 100081, 107667

Offset: 0

Author

Gary W. Adamson, Aug 29 2008

Keywords

• nonn
• easy

Comments

Binomial transform of [1, 6, 14, 9, 0, 0, 0,...].

Row sums of triangle A033292.

Examples

			a(3) = 70 = (1, 3, 3, 1) dot (1, 6, 14, 9) = (1 + 18 + 42 + 9). a(3) = 70 = sum of row 3 terms of triangle A033292: (13 + 16 + 19, + 22).
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A000292, A000326, A002412, A033292.

Cf. A226449. - Bruno Berselli, Jun 09 2013

Programs

Mathematica

Table[(n+1)*(3*n^2+2*n+2)/2, {n,0,50}] (* G. C. Greubel, May 30 2021 *)

Sage

[(n+1)*(3*n^2+2*n+2)/2 for n in (0..50)] # G. C. Greubel, May 30 2021

Formula

From R. J. Mathar, Aug 29 2008: (Start)

G.f.: (1 +3*x +5*x^2)/(1-x)^4.

a(n) = A002412(n+1) + 5*A000292(n-1). (End)

a(n) = A000326(n+1) + (n+1)*A000326(n). - Bruno Berselli, Jun 07 2013

From G. C. Greubel, May 30 2021: (Start)

a(n) = (n+1)*(3*n^2 +2*n +2)/2.

E.g.f.: (1/2)*(2 +12*x +14*x^2 +3*x^3)*exp(x). (End)

Extensions

Extended beyond a(14) by R. J. Mathar, Aug 29 2008