A288487 Cuboids that fit in square rings from A288486 obtaining a fifth power.

1, 8, 75, 400, 1445, 4056, 9583, 20000, 38025, 67240, 112211, 178608, 273325, 404600, 582135, 817216, 1122833, 1513800, 2006875, 2620880, 3376821, 4298008, 5410175, 6741600, 8323225, 10188776, 12374883, 14921200, 17870525, 21268920, 25165831, 29614208

Offset

0,2

Comments

If we add a(n) and A288487(n) graphically we obtain a bigger cuboid which is a square of cubes (a cuboid with dimensions n^2 * n^2 * n).

a(10^n) is a palindrome in base 10.

Links

Daniel Poveda Parrilla, Table of n, a(n) for n = 0..10000

Daniel Poveda Parrilla, Illustration of initial terms

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

G.f.: (1 + 2*x + 42*x^2 + 50*x^3 + 25*x^4)/(1 - x)^6.

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6).

a(n) = (n + 1)*(n^2 + 1)^2 = (n + 1)*(A002522(n))^2 = (n + 1)*A082044(n).

a(n) = n^5 + A002061(A002061(n+1)).

a(n) = A000584(n+1) - A288486(n)

a(n) = (n + 1)*A059100(n-1) + 4*(n^2 -1)*A014206(n-1) for n > 1.

Mathematica

Table[(1 + n)*(1 + n^2)^2, {n, 0, 28}] (* or *) CoefficientList[Series[(1 + 2 x + 42 x^2 + 50 x^3 + 25 x^4)/(1 - x)^6, {x, 0, 28}], x] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 8, 75, 400, 1445, 4056}, 29]

Prog

(PARI) Vec((1 + 2*x + 42*x^2 + 50*x^3 + 25*x^4)/(1 - x)^6) + O(x^28))

Crossrefs

Cf. A000584, A002061, A002522, A014206, A059100, A082044, A288486.

Sequence in context: A116251 A166084 A123661 * A123003 A015578 A145600

Adjacent sequences: A288484 A288485 A288486 * A288488 A288489 A288490

Keyword

nonn,easy

Author

Daniel Poveda Parrilla, Jun 11 2017

Status

approved