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A196514 Partial sums of A100381. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 10 04:15 EST 2019. Contains 329885 sequences. (Running on oeis4.)