A196514 Partial sums of A100381.

0, 4, 28, 124, 444, 1404, 4092, 11260, 29692, 75772, 188412, 458748, 1097724, 2588668, 6029308, 13893628, 31719420, 71827452, 161480700, 360710140, 801112060, 1769996284, 3892314108, 8522825724, 18589155324, 40399536124, 87509958652

Offset

0,2

Comments

Like any sequence with a linear recurrence, this has a Pisano period length modulo any k >= 1. The period lengths for this sequence are (modulo k >= 1) 1, 1, 6, 1, 20, 6, 21, 1, 18, 20, 110, 6, 156, 21, 60, 1, 136, 18, 342, 20, ....

References

Jolley, Summation of Series, Dover (1961), eq (53) page 10.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..3000

Index entries for linear recurrences with constant coefficients, signature (7,-18,20,-8).

Formula

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

a(n) = (n^2 - n + 2)*2^(n+1) - 4 = 4*A055580(n-1).

a(n) = 7*a(n-1) - 18*a(n-2) + 20*a(n-3) - 8*a(n-4); a(0)=0, a(1)=4, a(2)=28, a(3)=124. - Harvey P. Dale, Jan 12 2016

Mathematica

Table[2^n*Binomial[n, 2], {n, 1, 27}] // Accumulate (* Jean-François Alcover, Jun 24 2013 *)
LinearRecurrence[{7, -18, 20, -8}, {0, 4, 28, 124}, 30] (* Harvey P. Dale, Jan 12 2016 *)

Prog

(Magma) [(n^2-n+2)*2^(n+1)-4 : n in [0..30]]; // Vincenzo Librandi, Oct 05 2011
(PARI) a(n)=(n^2-n+2)<<(n+1)-4 \\ Charles R Greathouse IV, Oct 05 2011

Crossrefs

Sequence in context: A318011 A328685 A212900 * A249629 A131459 A231581

Adjacent sequences: A196511 A196512 A196513 * A196515 A196516 A196517

Keyword

nonn,easy,less

Author

R. J. Mathar, Oct 03 2011

Status

approved