OFFSET
0,2
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
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1)
FORMULA
a(n) = (10*n + 7)*binomial(n+6, 6)/7.
G.f.: (1+9*x)/(1-x)^8.
From G. C. Greubel, Jan 19 2020: (Start)
a(n) = 10*binomial(n+7, 7) - 9*binomial(n+6, 6).
E.g.f.: (7! + 80640*x + 189000*x^2 + 142800*x^3 + 45150*x^4 + 6552*x^5 + 427*x^6 + 10*x^7)*exp(x)/7!. (End)
a(n) = 8*a(n-1)-28*a(n-2)+56*a(n-3)-70*a(n-4)+56*a(n-5)-28*a(n-6)+8*a(n-7)-a(n-8). - Wesley Ivan Hurt, Nov 28 2021
MAPLE
seq( (10*n+7)*binomial(n+6, 6)/7, n=0..30); # G. C. Greubel, Jan 19 2020
MATHEMATICA
Table[10*Binomial[n+7, 7] -9*Binomial[n+6, 6], {n, 0, 30}] (* G. C. Greubel, Jan 19 2020 *)
Rest[Nest[Accumulate[#]&, Table[n(n+1)(10n-7)/6, {n, 0, 50}], 4]] (* Harvey P. Dale, Aug 03 2020 *)
PROG
(PARI) vector(31, n, (10*n-3)*binomial(n+5, 6)/7) \\ G. C. Greubel, Jan 19 2020
(Magma) [(10*n+7)*Binomial(n+6, 6)/7: n in [0..30]]; // G. C. Greubel, Jan 19 2020
(Sage) [(10*n+7)*binomial(n+6, 6)/7 for n in (0..30)] # G. C. Greubel, Jan 19 2020
(GAP) List([0..30], n-> (10*n+7)*Binomial(n+6, 6)/7 ); # G. C. Greubel, Jan 19 2020
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Feb 03 2000
STATUS
approved