A081587 Third row of Pascal-(1,4,1) array A081579.

1, 11, 46, 106, 191, 301, 436, 596, 781, 991, 1226, 1486, 1771, 2081, 2416, 2776, 3161, 3571, 4006, 4466, 4951, 5461, 5996, 6556, 7141, 7751, 8386, 9046, 9731, 10441, 11176, 11936, 12721, 13531, 14366, 15226, 16111, 17021, 17956, 18916, 19901

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = (2 - 5*n + 25*n^2)/2.

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

a(n) = a(n-1) + 25*n - 15 with a(0)=1. - Vincenzo Librandi, Aug 08 2010

E.g.f.: (1/2)*(2 + 20*x + 25*x^2)*exp(x). - G. C. Greubel, May 26 2021

Example

a(1)=25*1+1-15=11; a(2)=25*2+11-15=46; a(3)=25*3+46-15=106.

Mathematica

((10*Range[0, 40]-1)^2 +7)/8 (* G. C. Greubel, May 26 2021 *)

Prog

(PARI) a(n)=5*n*(5*n-1)/2+1 \\ Charles R Greathouse IV, Jun 16 2017
(Magma) [(2-5*n+25*n^2)/2: n in [0..50]]; // G. C. Greubel, May 26 2021
(Sage) [((10*n-1)^2 +7)/8 for n in (0..40)] # G. C. Greubel, May 26 2021

Crossrefs

Cf. A016861, A081588.

Sequence in context: A116193 A282095 A063158 * A377663 A223834 A359096

Adjacent sequences: A081584 A081585 A081586 * A081588 A081589 A081590

Keyword

easy,nonn

Author

Paul Barry, Mar 23 2003

Status

approved