



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
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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 / ( (x1)*(2*x1)^3 ).
a(n) = (n^2  n + 2)*2^(n+1)  4 = 4*A055580(n1).
a(n) = 7*a(n1)  18*a(n2) + 20*a(n3)  8*a(n4); 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 (* JeanFrançois Alcover, Jun 24 2013 *)
LinearRecurrence[{7, 18, 20, 8}, {0, 4, 28, 124}, 30] (* Harvey P. Dale, Jan 12 2016 *)


PROG

(MAGMA) [(n^2n+2)*2^(n+1)4 : n in [0..30]]; // Vincenzo Librandi, Oct 05 2011
(PARI) a(n)=(n^2n+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



