A346007 Let b=5. If n == -i (mod b) for 0 <= i < b, then a(n) = binomial(b,i+1)*((n+i)/b)^(i+1).

0, 1, 5, 10, 10, 5, 32, 80, 80, 40, 10, 243, 405, 270, 90, 15, 1024, 1280, 640, 160, 20, 3125, 3125, 1250, 250, 25, 7776, 6480, 2160, 360, 30, 16807, 12005, 3430, 490, 35, 32768, 20480, 5120, 640, 40, 59049, 32805, 7290, 810, 45, 100000, 50000, 10000, 1000, 50

Offset

0,3

Comments

These are the numbers that would arise if the Moessner construction on page 64 of Conway-Guy's "Book of Numbers" were extended to the fifth powers.

References

J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996. See pp. 63-64.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,6,0,0,0,0,-15,0,0,0,0,20,0,0,0,0,-15,0,0,0,0,6,0,0,0,0,-1).

Formula

G.f.: x*(1 + 5*x + 10*x^2 + 10*x^3 + 5*x^4 + 26*x^5 + 50*x^6 + 20*x^7 - 20*x^8 - 20*x^9 + 66*x^10 - 60*x^12 + 30*x^14 + 26*x^15 - 50*x^16 + 20*x^17 + 20*x^18 - 20*x^19 + x^20 - 5*x^21 + 10*x^22 - 10*x^23 + 5*x^24)/((1 - x)^6*(1 + x + x^2 + x^3 + x^4)^6). - Andrew Howroyd, Nov 12 2025

Maple

f:=proc(n, b) local i;
for i from 0 to b-1 do
if ((n+i) mod b) = 0 then return(binomial(b, i+1)*((n+i)/b)^(i+1)); fi;
od;
end;
[seq(f(n, 5), n=0..80)];

Prog

(Python)
from sympy import binomial
def A346007(n):
    i = (5-n)%5
    return binomial(5, i+1)*((n+i)//5)**(i+1) # Chai Wah Wu, Jul 25 2021
(PARI) a(n) = { my(r=(-n)%5); binomial(5, r+1)*((n+r)/5)^(r+1) } \\ Andrew Howroyd, Nov 12 2025

Crossrefs

Setting b = 2, 3, or 4 gives A346004, A346005, and A346006.

Cf. A125714, A346595.

Sequence in context: A280718 A321357 A065755 * A135912 A200990 A040020

Adjacent sequences: A346004 A346005 A346006 * A346008 A346009 A346010

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 25 2021

Status

approved