A176640 Partial sums of A005985.

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

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