A115127 Second (k=2) triangle of numbers related to totally asymmetric exclusion process (case alpha=1, beta=1).
3, 6, 7, 10, 16, 19, 15, 30, 47, 56, 21, 50, 95, 146, 174, 28, 77, 170, 311, 471, 561, 36, 112, 280, 586, 1043, 1562, 1859, 45, 156, 434, 1015, 2044, 3564, 5291, 6292, 55, 210, 642, 1652, 3682, 7204, 12363, 18226, 21658, 66, 275, 915, 2562, 6230, 13392, 25623
Offset: 2
Examples
[3];[6,7];[10,16,19];[15,30,47,56];... Main diagonal (n-m=1) example: a(3,2)= 7 = 5 + 2 because A115126(3,2)=5 and A115126(2,2)=2. Subdiagonal (n-m>1) example: a(4,2)= 16 = 9 + 7 because A115126(4,2)=9 and a(3,2)=7.
Links
- W. Lang: First 10 rows.
Crossrefs
Row sums give A115128.
Formula
A115130 Partial sums of A005557.
42, 174, 471, 1043, 2044, 3682, 6230, 10038, 15546, 23298, 33957, 48321, 67340, 92134, 124012, 164492, 215322, 278502, 356307, 451311, 566412, 704858, 870274, 1066690, 1298570, 1570842, 1888929, 2258781, 2686908, 3180414, 3747032
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Mathematica
Accumulate[LinearRecurrence[{6,-15,20,-15,6,-1},{42,132,297,572,1001,1638},40]] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{42,174,471,1043,2044,3682,6230},40] (* Harvey P. Dale, Feb 22 2024 *)
Formula
G.f.: (42-120*x+135*x^2-70*x^3+14*x^4)/(1-x)^7.
a(n)=A115127(n+5, 5), n>=1.
Comments