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
Examples
a(1)=25*1+1-15=11; a(2)=25*2+11-15=46; a(3)=25*3+46-15=106.
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).
Programs
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Magma
[(2-5*n+25*n^2)/2: n in [0..50]]; // G. C. Greubel, May 26 2021
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Mathematica
((10*Range[0,40]-1)^2 +7)/8 (* G. C. Greubel, May 26 2021 *)
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PARI
a(n)=5*n*(5*n-1)/2+1 \\ Charles R Greathouse IV, Jun 16 2017
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Sage
[((10*n-1)^2 +7)/8 for n in (0..40)] # G. C. Greubel, May 26 2021
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