A256718 a(n) = n*(n+1)*(7*n-6)/2.

0, 1, 24, 90, 220, 435, 756, 1204, 1800, 2565, 3520, 4686, 6084, 7735, 9660, 11880, 14416, 17289, 20520, 24130, 28140, 32571, 37444, 42780, 48600, 54925, 61776, 69174, 77140, 85695, 94860, 104656, 115104, 126225, 138040, 150570, 163836, 177859, 192660

Offset: 0

Author

Bruno Berselli, Apr 09 2015

Keywords

• nonn
• easy

References

• E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (21st row of the table).

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Partial sums of A051875.

Cf. similar sequences listed in A237616.

Programs

Magma

[n*(n+1)*(7*n-6)/2: n in [0..40]];

Mathematica

Table[n (n + 1) (7 n - 6)/2, {n, 0, 40}]
LinearRecurrence[{4,-6,4,-1},{0,1,24,90},40] (* Harvey P. Dale, Jan 15 2024 *)

PARI

vector(40, n, n--; n*(n+1)*(7*n-6)/2)

Sage

[n*(n+1)*(7*n-6)/2 for n in (0..40)]

Formula

G.f.: x*(1 + 20*x)/(1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with n>3, a(0)=0, a(1)=1, a(2)=24, a(3)=90.

a(n) = Sum_{i=0..n-1} (n-i)*(21*i+1) for n>0.