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A052150 Partial sums of A000340, second partial sums of A003462. 3
1, 6, 24, 82, 261, 804, 2440, 7356, 22113, 66394, 199248, 597822, 1793557, 5380776, 16142448, 48427480, 145282593, 435847950, 1307544040, 3922632330, 11767897221, 35303691916, 105911076024, 317733228372, 953199685441 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.

P. Ribenhoim, The Little Book of Big Primes, Springer-Verlag, N.Y., 1991, p. 53.

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (6,-12,10,-3).

FORMULA

a(n) = ((3^(n+3)) - (2*(n^2) + 12n + 19))/8.

a(n) = sum{k=0..n, binomial(n+3, k+3)2^k}. - Paul Barry, Aug 20 2004

From Colin Barker, Dec 18 2012: (Start)

a(n) = 6*a(n-1) - 12*a(n-2) + 10*a(n-3) - 3*a(n-4).

G.f.: 1/((x-1)^3*(3*x-1)). (End)

EXAMPLE

a(n)=3a(n-1)+C(n+2,2); a(0)=1.

MATHEMATICA

LinearRecurrence[{6, -12, 10, -3}, {1, 6, 24, 82}, 40] (* Harvey P. Dale, Sep 05 2013 *)

CROSSREFS

Cf. A003462, A000340.

Sequence in context: A320856 A047790 A133474 * A118043 A317408 A166060

Adjacent sequences:  A052147 A052148 A052149 * A052151 A052152 A052153

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jan 23 2000

STATUS

approved

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Last modified February 18 09:42 EST 2019. Contains 320249 sequences. (Running on oeis4.)