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

0,3

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).

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.

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 *)

Prog

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

Crossrefs

Partial sums of A051875.

Cf. similar sequences listed in A237616.

Sequence in context: A305888 A233644 A010012 * A233637 A179962 A076799

Adjacent sequences: A256715 A256716 A256717 * A256719 A256720 A256721

Keyword

nonn,easy

Author

Bruno Berselli, Apr 09 2015

Status

approved