A144335 Row sums of triangle A144334, binomial transform of [1, 2, 6, 7, 3, 0, 0, 0, ...].
1, 3, 11, 32, 76, 156, 288, 491, 787, 1201, 1761, 2498, 3446, 4642, 6126, 7941, 10133, 12751, 15847, 19476, 23696, 28568, 34156, 40527, 47751, 55901, 65053, 75286, 86682, 99326, 113306, 128713, 145641, 164187, 184451, 206536, 230548, 256596
Offset: 1
Examples
a(5) = 76 = (1, 4, 6, 4, 1) dot (1, 2, 6, 3, 7) = (1 + 8 + 36, + 28 + 3). a(3) = 11 = sum of row 3 terms of triangle A144334: (4 + 3 + 4).
Links
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Crossrefs
Cf. A144334.
Programs
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Mathematica
Table[1-5n/12+3n^2/8-n^3/12+n^4/8,{n,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{1,3,11,32,76},40] (* Harvey P. Dale, Aug 22 2016 *) -
PARI
a(n)=1-(5/12)*n+(3/8)*n^2-(1/12)*n^3+(1/8)*n^4 \\ Charles R Greathouse IV, Oct 21 2022
Formula
G.f.: (1 - 2x + 6x^2 - 3x^3 + x^4)*x/(1-x)^5.
a(n) = 1 - (5/12)*n + (3/8)*n^2 - (1/12)*n^3 + (1/8)*n^4. - R. J. Mathar, Sep 18 2008
Extensions
Extended by R. J. Mathar, Sep 18 2008