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!)
 A145069 a(n) = n*(n^2 + 3*n + 5)/3. 1
 0, 3, 10, 23, 44, 75, 118, 175, 248, 339, 450, 583, 740, 923, 1134, 1375, 1648, 1955, 2298, 2679, 3100, 3563, 4070, 4623, 5224, 5875, 6578, 7335, 8148, 9019, 9950, 10943, 12000, 13123, 14314, 15575, 16908, 18315, 19798, 21359, 23000, 24723, 26530 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Old name was: Partial sums of A002061, starting at n=2. Number of floating point dot operations (multiplications and divisions) in the factorization of an (n+1) X (n+1) real matrix by Gaussian elimination as, e.g., implemented in LINPACK subroutines sgefa.f or dgefa.f. The number of multiplications alone is given by A007290. The number of additions is given by A000330. - Hugo Pfoertner, Mar 28 2018 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 (corrected by Ray Chandler, Jan 19 2019) Cleve Moler, LINPACK subroutine sgefa.f, University of New Mexico, Argonne National Lab, 1978. Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). FORMULA G.f.: x*(3-2*x+x^2)/(1-x)^4. a(n) = Sum_{j=2..n+1} A002061(j). a(n) = a(n-1) + n^2 + n + 1 for n > 0, with a(0) = 0. a(n) = n*(n^2+3*n+5)/3. - Bruno Berselli, Apr 01 2011 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 30 2012 a(n) = Sum_{i=1..n} 3i+(n-i)^2. - Wesley Ivan Hurt, Aug 21 2014 a(n) = A007290(n+2) + n. - Hugo Pfoertner, Mar 28 2018 EXAMPLE a(2) = a(1) + 2^2 + 2 + 1 = 3 + 4 + 2 + 1 = 10. a(3) = a(2) + 3^2 + 3 + 1 = 10 + 9 + 3 + 1 = 23. MAPLE A145069:=n->n*(n^2+3*n+5)/3: seq(A145069(n), n=0..100); # Wesley Ivan Hurt, Aug 21 2014 MATHEMATICA lst={}; s=0; Do[s+=n^2+n+1; AppendTo[lst, s-1], {n, 0, 5!}]; lst CoefficientList[Series[x(3-2*x+x^2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 30 2012 *) Table[n (n^2+3n+5)/3, {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {0, 3, 10, 23}, 50] (* Harvey P. Dale, Sep 10 2016 *) PROG (PARI) {a=0; for(n=1, 42, print1(a, ", "); a=a+n^2+n+1)} \\ adapted by Michel Marcus, Aug 23 2014 (MAGMA) I:=[0, 3, 10, 23]; [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..50]]; // Vincenzo Librandi, Jun 30 2012 CROSSREFS Cf. A002061 (n^2 - n + 1). Cf. A028387 (n + (n+1)^2). Cf. A077415 (zero followed by partial sums of A028387, starting at n=1). Cf. A007290. Sequence in context: A172112 A227347 A068043 * A293350 A256525 A192973 Adjacent sequences:  A145066 A145067 A145068 * A145070 A145071 A145072 KEYWORD nonn,easy AUTHOR Vladimir Joseph Stephan Orlovsky, Sep 30 2008 EXTENSIONS Edited by Klaus Brockhaus, Oct 21 2008 G.f. adapted to the offset by Bruno Berselli, Apr 01 2011 Name, offset, and formulas changed by Wesley Ivan Hurt, Aug 21 2014 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 July 9 01:30 EDT 2020. Contains 335537 sequences. (Running on oeis4.)