A108496 -id:A108496 - cp's OEIS frontend

A108497 Triangle read by rows: T(n,k) = k^(n+1)-k mod n, showing 1<=k<=n.

0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 6, 5, 6, 2, 0, 0, 6, 0, 4, 0, 2, 0, 0, 0, 5, 6, 0, 8, 3, 0, 2, 0, 0, 6, 4, 0, 0, 0, 6, 4, 0, 0, 0, 2, 6, 1, 9, 8, 9, 1, 6, 2, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 2, 6, 12, 7, 4, 3, 4, 7, 12, 6, 2, 0, 0, 6, 10, 4, 8, 0, 0, 0, 6, 10, 4, 8

Offset: 1

Henry Bottomley, Jun 06 2005

			Rows start: 0; 0,0; 0,2,0; 0,2,0,0; 0,2,1,2,0; 0,0,0,0,0,0; 0,2,6,5,6,2,0; etc.
T(7,3) = 3^(7+1)-3 mod 7 = 6558 mod 7 = 6.

Cf. A014117, A108495, A108496, A108498, A108499.

T(n, k+n)=T(n, k). T(n, 0)=T(n, 1)=T(n, n)=T(1, k)=T(2, k)=T(6, k)=T(42, k)=T(1806, k)=0.

A108495 a(n) = (n^7 - n)/6.

Original entry on oeis.org

0, 0, 21, 364, 2730, 13020, 46655, 137256, 349524, 797160, 1666665, 3247860, 5971966, 10458084, 17568915, 28476560, 44739240, 68389776, 102036669, 148978620, 213333330, 300181420, 415726311, 567470904, 764411900, 1017252600

Offset: 0

Henry Bottomley, Jun 06 2005

Also integer sequences for (n^2-n)/1 (A002378 offset), (n^3-n)/2 (A027480 offset), (n^43-n)/42 (A108496) and (n^1807-n)/1806.

			a(2) = (2^7 - 2)/6 = 126/6 = 21.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
D. Zagier, Problems posed at the St Andrews Colloquium, 1996.
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A014117, A108497, A108499.

[(n^7-n)/6: n in [0..40]]; // Vincenzo Librandi, May 02 2011

Table[(n^7-n)/6,{n,0,30}] (* or *) LinearRecurrence[ {8,-28,56,-70,56,-28,8,-1},{0,0,21,364,2730,13020,46655,137256},30] (* Harvey P. Dale, Apr 16 2014 *)

[(n**7-n)//6 for n in range(41)] # David Radcliffe, Jun 06 2025

a(n) = (n-1)*A059721(n) = -A024004(n)*n/6.

G.f.: 7*x^2*(3 + 28*x + 58*x^2 + 28*x^3 + 3*x^4)/(1-x)^8. [Colin Barker, May 08 2012]

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A108497 Triangle read by rows: T(n,k) = k^(n+1)-k mod n, showing 1<=k<=n.

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A108495 a(n) = (n^7 - n)/6.

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