This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A109620 a(n) = (1/3)*n^3 - n^2 - (1/3)*n - 1. 0
 -1, -2, -3, -2, 3, 14, 33, 62, 103, 158, 229, 318, 427, 558, 713, 894, 1103, 1342, 1613, 1918, 2259, 2638, 3057, 3518, 4023, 4574, 5173, 5822, 6523, 7278, 8089, 8958, 9887, 10878, 11933, 13054, 14243, 15502, 16833, 18238, 19719, 21278, 22917, 24638, 26443, 28334, 30313, 32382, 34543, 36798 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS It is interesting that this sequence is generated using the same rules as those given for A108618 (version "jes"; the initial seed is the floretion given in program code, below). In reference to those rules, we have: **Loop 0** + .5'i + .5i' + .5'ik' + .5'ji' + e **Loop 1** + 1.5'i - .5'j + 1.5i' - .5k' + .5'ii' + 1.5'ik' + 1.5'ji' + .5'kj' + 3e **Loop 2** + 3.5'i - 2'j + 3.5i' - 2k' + 2'ii' + 3.5'ik' + 3.5'ji' + 2'kj' + 5e **Loop 3** + 6.5'i - 5.5'j + 6.5i' - 5.5k' + 5.5'ii' + 6.5'ik' + 6.5'ji' + 5.5'kj' + 7e **Loop 4** + 10.5'i - 12'j + 10.5i' - 12k' + 12'ii' + 10.5'ik' + 10.5'ji' + 12'kj' + 9e **Loop 5** + 15.5'i - 22.5'j + 15.5i' - 22.5k' + 22.5'ii' + 15.5'ik' + 15.5'ji' + 22.5'kj' + 11e **Loop 6** + 21.5'i - 38'j + 21.5i' - 38k' + 38'ii' + 21.5'ik' + 21.5'ji' + 38'kj' + 13e **Loop 7** + 28.5'i - 59.5'j + 28.5i' - 59.5k' + 59.5'ii' + 28.5'ik' + 28.5'ji' + 59.5'kj' + 15e **Loop 8** + 36.5'i - 88'j + 36.5i' - 88k' + 88'ii' + 36.5'ik' + 36.5'ji' + 88'kj' + 17e **Loop 9** + 45.5'i - 124.5'j + 45.5i' - 124.5k' + 124.5'ii' + 45.5'ik' + 45.5'ji' + 124.5'kj' + 19e. a(n) is calculated by adding the real number coefficients of 'i, 'j and 'k (which is always 0 here) from the n-th loop and multiplying the result by -2. LINKS Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1). FORMULA a(n) = A006527(n) - A002061(n+1), g.f. (2*x-1)*(x^2+1)/(x-1)^4 a(0)=-1, a(1)=-2, a(2)=-3, a(3)=-2, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)- a(n-4). - Harvey P. Dale, Jul 21 2013 MAPLE seriestolist(series((2*x-1)*(x^2+1)/(x-1)^4, x=0, 50)); -or- Floretion Algebra Multiplication Program, FAMP Code: -2jessumseq[ + .5'i + .5i' + .5'ik' + .5'ji' + e], Sumtype: sum[Y[15]] = sum[ * ]. Note: 2ibasesumseq = A002061, apart from initial term, -2jbasesumseq = A006527. MATHEMATICA Table[n^3/3-n^2-n/3-1, {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {-1, -2, -3, -2}, 60] (* Harvey P. Dale, Jul 21 2013 *) CROSSREFS Cf. A006527, A002061. Sequence in context: A223168 A077942 A077989 * A138781 A224416 A282049 Adjacent sequences:  A109617 A109618 A109619 * A109621 A109622 A109623 KEYWORD easy,sign AUTHOR Creighton Dement, Aug 01 2005 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.