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A176640 Partial sums of A005985. 0
0, 1, 5, 14, 46, 111, 303, 688, 1712, 3761, 8881, 19122, 43698, 92851, 207539, 436916, 961204, 2009781, 4369077, 9087670, 19573430, 40544951, 86682295, 178956984, 380283576, 782936761, 1655351993, 3400182458, 7158278842 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums of length of longest walk on edges of n-cube. The subsequence of primes in this partial sum begins: 5, 3761, 40544951.

LINKS

Table of n, a(n) for n=0..28.

Index entries for linear recurrences with constant coefficients, signature (3,3,-15,6,12,-8).

FORMULA

a(n) = SUM[i=0..n] A005985(i).

Empirical G.f.: x*(1+2*x-4*x^2+4*x^3)/((1-x)^2*(1+x)*(1-2*x)^2*(1+2*x)). [Colin Barker, Jan 14 2012]

a(0)=0, a(1)=1, a(2)=5, a(3)=14, a(4)=46, a(5)=111, a(n)=3*a(n-1)+ 3*a(n-2)- 15*a(n-3)+ 6*a(n-4)+12*a(n-5)-8*a(n-6). - Harvey P. Dale, Jun 11 2015

EXAMPLE

a(21) = 0 + 1 + 4 + 9 + 32 + 65 + 192 + 385 + 1024 + 2049 + 5120 + 10241 + 24576 + 49153 + 114688 + 229377 + 524288 + 1048577 + 2359296 + 4718593 + 10485760 + 20971521 = 40544951 is prime.

MATHEMATICA

Accumulate[LinearRecurrence[{2, 5, -10, -4, 8}, {0, 1, 4, 9, 32}, 40]] (* or *) LinearRecurrence[{3, 3, -15, 6, 12, -8}, {0, 1, 5, 14, 46, 111}, 40] (* Harvey P. Dale, Jun 11 2015 *)

CROSSREFS

Cf. A005985.

Sequence in context: A270620 A270636 A077335 * A126729 A336006 A098730

Adjacent sequences:  A176637 A176638 A176639 * A176641 A176642 A176643

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Apr 22 2010

STATUS

approved

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Last modified October 3 22:17 EDT 2022. Contains 357237 sequences. (Running on oeis4.)