A196513 a(n) = 1*4*7 + 4*7*10 + 7*10*13 + ... (n terms).

0, 28, 308, 1218, 3298, 7250, 13938, 24388, 39788, 61488, 91000, 129998, 180318, 243958, 323078, 420000, 537208, 677348, 843228, 1037818, 1264250, 1525818, 1825978, 2168348, 2556708, 2995000, 3487328, 4037958, 4651318, 5331998, 6084750

Offset

0,2

References

Jolley, Summation of Series, Dover (1961), eq (49) page 10.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1)

Formula

a(n) = ((3*n-2)*(3*n+1)*(3*n+4)*(3*n+7) + 56)/12 = n*(3*n+5)*(9*n^2 + 15*n - 10)/4 = Sum_{i=1..n} (3*i-2)*(3*i+1)*(3*i+4).

G.f.: -2*x*(14 + 84*x - 21*x^2 + 4*x^3) / (x-1)^5.

Prog

(Magma) [n*(3*n+5)*(9*n^2+15*n-10)/4 : n in [0..30]]; // Vincenzo Librandi, Oct 05 2011

Crossrefs

Sequence in context: A107942 A219172 A334882 * A042520 A022688 A125416

Adjacent sequences: A196510 A196511 A196512 * A196514 A196515 A196516

Keyword

nonn,easy

Author

R. J. Mathar, Oct 03 2011

Status

approved