The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A147656 The arithmetic mean of the n-th and (n+1)-st cubes, rounded down. 1
 0, 4, 17, 45, 94, 170, 279, 427, 620, 864, 1165, 1529, 1962, 2470, 3059, 3735, 4504, 5372, 6345, 7429, 8630, 9954, 11407, 12995, 14724, 16600, 18629, 20817, 23170, 25694, 28395, 31279, 34352, 37620, 41089, 44765, 48654, 52762, 57095, 61659 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The terms of this sequence relate to intervals between cubes in the same fashion as terms of A002378 are related to intervals between squares. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA a(n) = floor((A000578(n) + A000578(n+1))/2). From R. J. Mathar, Nov 11 2008: (Start) a(n) = A000578(n) + A045943(n) = n*(2n^2+3n+3)/2. G.f.: x*(4+x+x^2)/(1-x)^4. (End) a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, May 06 2012 a(n) = A027480(n) + A006003(n). - Bruce J. Nicholson, Jun 03 2018 From A.H.M. Smeets, Sep 10 2018: (Start) a(n) = Sum_{k=0..n-1} (n+1)^2-k for n >= 0 with empty domain of summation for n = 0. a(n) = n*(n+1)^2 - n*(n-1)/2 for n >= 0. Lim_{n -> inf} a(n-1)/n^3 = 1. (End) E.g.f.: exp(x)*(8*x + 9*x^2 + 2*x^3)/2. - Stefano Spezia, Sep 12 2018 a(n) = A081435(n)-1. - R. J. Mathar, Sep 14 2018 MAPLE seq(coeff(series(x*(x^2+x+4)/(1-x)^4, x, n+1), x, n), n = 0 .. 40); # Muniru A Asiru, Sep 11 2018 MATHEMATICA Table[(n^3+(n+1)^3-1)/2, {n, 0, 70}] (* Vladimir Joseph Stephan Orlovsky, May 04 2011 *) PROG (PARI) j=[]; for (n=0, 40, j=concat(j, n^3+floor(((n+1)^3 - n^3)/2))); j (PARI) a(n) = n*(2*n^2+3*n+3)/2; \\ Altug Alkan, Sep 20 2018 (MAGMA) I:=[0, 4, 17, 45]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, May 06 2012 CROSSREFS Cf. A000578. Cf. A027480, A006003. Sequence in context: A212575 A162148 A166781 * A095667 A212577 A332863 Adjacent sequences:  A147653 A147654 A147655 * A147657 A147658 A147659 KEYWORD nonn,easy AUTHOR Alexander R. Povolotsky, Nov 09 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 21 00:57 EDT 2021. Contains 345329 sequences. (Running on oeis4.)