

A225209


a(n) = (392*16^n 1620*8^n +1890*4^n 767)/105.


1



1, 249, 8537, 186073, 3427545, 58664153, 970097881, 15776875737, 254486643929, 4088295982297, 65545039643865, 1049779971687641, 16804957869966553, 268947166998693081, 4303697458594972889, 68863501862374868185
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OFFSET

1,2


COMMENTS

Starting at n=1, a cube has an edge=2^(n+1)3. The beginning cube has a value of 1 and is surrounded by 2^n layers of cubes each valued at 2^n. The sum of all cubes with values of 2^n is a(n).
Indices of primes in this sequence: 3, 10, 12, 21, 37, 70, 102, 201, 961, 1854, ....


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..825
Index entries for linear recurrences with constant coefficients, signature (29,252,736,512).


FORMULA

a(n) = 29*a(n1)  252*a(n2) + 736*a(n3)  512*a(n4).
a(n) = a(n1) + 7*2^(4*n1)  27*2^(3*n1) + 27*2^(2*n1), for n>0.
G.f. x*(1 +220*x +1568*x^2 +512*x^3)/( (1x)*(14*x)*(18*x)*(116*x) ).  R. J. Mathar, May 09 2013
a(n) = a(n1) +2^(n1)*(A036563(n+1)^3 A036563(n)^3).  R. J. Mathar, May 18 2013


EXAMPLE

The first cubes has value 1=a(1). The second cube has 2 layers of cubes each valued at 2 surrounding the cube of value 1 to give (5^31)*2+1=249=a(2). Next surround by 2^2 layers of cubes each valued at 2^2: (13^35^3)*4+249=8537=a(3). Finally, surround by 2^3 layers of cubes each of value 2^3 to get (29^313^3)*8 + 8537 = 186073 = a(4).


MAPLE

seq( (392*2^(4*n) 1620*2^(3*n) +1890*2^(2*n) 767)/105, n=1..20); # G. C. Greubel, Dec 31 2019


MATHEMATICA

LinearRecurrence[{29, 252, 736, 512}, {1, 249, 8537, 186073}, 20] (* Harvey P. Dale, Apr 22 2018 *)


PROG

(PARI) vector(20, n, (392*2^(4*n) 1620*2^(3*n) +1890*2^(2*n) 767)/105) \\ G. C. Greubel, Dec 31 2019
(Magma) [(392*2^(4*n) 1620*2^(3*n) +1890*2^(2*n) 767)/105: n in [1..20]]; // G. C. Greubel, Dec 31 2019
(Sage) [(392*2^(4*n) 1620*2^(3*n) +1890*2^(2*n) 767)/105 for n in (1..20)] # G. C. Greubel, Dec 31 2019
(GAP) List([1..20], n> (392*2^(4*n) 1620*2^(3*n) +1890*2^(2*n) 767)/105); # G. C. Greubel, Dec 31 2019


CROSSREFS

Sequence in context: A045254 A197349 A197400 * A197363 A069154 A045169
Adjacent sequences: A225206 A225207 A225208 * A225210 A225211 A225212


KEYWORD

nonn,easy


AUTHOR

J. M. Bergot, May 01 2013


STATUS

approved



