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A256718
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a(n) = n*(n+1)*(7*n-6)/2.
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2
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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
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OFFSET
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0,3
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REFERENCES
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E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (21st row of the table).
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LINKS
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Bruno Berselli, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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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.
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MATHEMATICA
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Table[n (n + 1) (7 n - 6)/2, {n, 0, 40}]
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PROG
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(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]];
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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Bruno Berselli, Apr 09 2015
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STATUS
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approved
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