OFFSET
0,1
COMMENTS
A floretion-generated sequence which arises from a particular transform of the centered square numbers: A001844. Specifically, (a(n)) is the jesfor-transform of the sequence A001844 with respect to the floretion given in the program code. The sequence relates centered square numbers, triangular numbers and centered octahedral numbers to (n+1)^3. Note: this was made possible in part by the formula already given for A085786.
Floretion Algebra Multiplication Program, FAMP Code: 4jesforseq[ + .25'j + .25'k + .25j' + .25k' + .25'ij' + .25'ik' + .25'ji' + .25'ki' + e ], vesforseq = A001844, ForType: 1A, LoopType: tes.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {2, 13, 43, 102}, 50] (* Paolo Xausa, Mar 09 2024 *)
PROG
(Magma) [(1/6)*(n+1)*(10*n^2+17*n+12): n in [0..50]]; // Vincenzo Librandi, May 30 2011
(PARI) a(n) = (n+1)*(10*n^2+17*n+12)/6
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Creighton Dement, Feb 19 2005
STATUS
approved