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 A052254 Partial sums of A050406. 3
 1, 17, 108, 444, 1410, 3762, 8844, 18876, 37323, 69355, 122408, 206856, 336804, 531012, 813960, 1217064, 1780053, 2552517, 3595636, 4984100, 6808230, 9176310, 12217140, 16082820, 20951775 (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. 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 Cf. A050406. Cf. A093645 ((10, 1) Pascal, column m=7). Sequence in context: A159031 A080441 A135400 * A156851 A141921 A013308 Adjacent sequences:  A052251 A052252 A052253 * A052255 A052256 A052257 KEYWORD easy,nonn AUTHOR Barry E. Williams, Feb 03 2000 STATUS approved

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Last modified June 29 09:21 EDT 2022. Contains 354910 sequences. (Running on oeis4.)