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A081587 Third row of Pascal-(1,4,1) array A081579. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A223834 A143059 A224142

Adjacent sequences:  A081584 A081585 A081586 * A081588 A081589 A081590

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 23 2003

STATUS

approved

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Last modified June 21 03:51 EDT 2021. Contains 345354 sequences. (Running on oeis4.)