A174814 a(n) = n*(n+1)*(5*n+1)/3.

0, 4, 22, 64, 140, 260, 434, 672, 984, 1380, 1870, 2464, 3172, 4004, 4970, 6080, 7344, 8772, 10374, 12160, 14140, 16324, 18722, 21344, 24200, 27300, 30654, 34272, 38164, 42340, 46810, 51584, 56672, 62084, 67830, 73920, 80364, 87172, 94354, 101920, 109880

Offset: 0

Author

Bruno Berselli, Dec 01 2010 - Dec 02 2010

Keywords

• nonn
• easy

Comments

Also zero followed by bisection (even part) of A088003.

Numbers ending in 0, 2 or 4 (cf. 2*A053796(n)). Therefore we can easily see that a(m)^(2*k+1)==-1 (mod 5) only for m in A047219, while a(m)^(2*k)==-1 (mod 5) only for m in A016873 and k odd.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Programs

Magma

[n*(n+1)*(5*n+1)/3: n in [0..50]]; // Vincenzo Librandi, May 30 2011

Mathematica

Table[1/3 n (1+n) (1+5 n), {n,0,50}]  (* Harvey P. Dale, Feb 25 2011 *)

PARI

a(n) = n*(n+1)*(5*n+1)/3 \\ Charles R Greathouse IV, May 30 2011

Formula

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

a(n) = 2*A033994(n) for n>0.

a(n) = n*A147875(n+1)-sum(k=1..n, A147875(k)) for n>0.

a(-n) = -A144945(n).