A052206 Partial sums of A050405.

1, 16, 100, 408, 1290, 3432, 8052, 17160, 33891, 62920, 110968, 187408, 304980, 480624, 736440, 1100784, 1609509, 2307360, 3249532, 4503400, 6150430, 8288280, 11033100, 14522040, 18915975

Offset: 0

Author

Barry E. Williams, Jan 28 2000

Keywords

• easy
• nonn

References

• A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
• Murray R.Spiegel, Calculus of Finite Differences and Difference Equations, "Schaum's Outline Series", McGraw-Hill, 1971, pp. 10-20, 79-94.

Links

• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A050405.

Cf. A093644 ((9, 1) Pascal, column m=7).

Programs

Mathematica

LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,16,100,408,1290,3432,8052,17160},30] (* Harvey P. Dale, May 28 2018 *)

Formula

a(n) = (9n+7)*C(n+6, 6)/7.

G.f.: (1+8*x)/(1-x)^8.