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A113841 a(n) = a(n-1) + 2^A047240(n) for n>1, a(1)=1. 1
1, 3, 7, 71, 199, 455, 4551, 12743, 29127, 291271, 815559, 1864135, 18641351, 52195783, 119304647, 1193046471, 3340530119, 7635497415, 76354974151, 213793927623, 488671834567, 4886718345671, 13682811367879, 31274997412295 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Vladimir Pletser, Congruence conditions on the number of terms in sums of consecutive squared integers equal to squared integers, arXiv:1409.7969 [math.NT], 2014.

Index entries for linear recurrences with constant coefficients, signature (1, 0, 64, -64).

FORMULA

G.f.: x*(1+2*x+4*x^2)/((-1+x)*(-1+4*x)*(1+4*x+16*x^2)). - Vaclav Kotesovec, Nov 28 2012

a(1)=1, a(2)=3, a(3)=7, a(4)=71, a(n)=a(n-1)+64*a(n-3)-64*a(n-4). - Harvey P. Dale, Nov 18 2013

MATHEMATICA

CoefficientList[Series[(1 + 2 x + 4 x^2) / ((-1 + x) (-1 + 4 x) (1 + 4 x + 16 x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, May 19 2013 *)

LinearRecurrence[{1, 0, 64, -64}, {1, 3, 7, 71}, 30] (* Harvey P. Dale, Nov 18 2013 *)

CROSSREFS

Cf. A099974, A112627, A080355, A080567, A099969, A099970, A099971.

Sequence in context: A127177 A261136 A127179 * A128072 A094008 A209477

Adjacent sequences:  A113838 A113839 A113840 * A113842 A113843 A113844

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Jan 27 2006

EXTENSIONS

Edited with better definition and offset corrected by Omar E. Pol, Jan 08 2009

STATUS

approved

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Last modified October 22 08:00 EDT 2019. Contains 328315 sequences. (Running on oeis4.)