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A175631 a(n) = (n-th pentagonal number) modulo (n-th triangular number). 0
0, 2, 0, 2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90, 104, 119, 135, 152, 170, 189, 209, 230, 252, 275, 299, 324, 350, 377, 405, 434, 464, 495, 527, 560, 594, 629, 665, 702, 740, 779, 819, 860, 902, 945, 989, 1034, 1080, 1127, 1175, 1224, 1274, 1325, 1377, 1430 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..55.

FORMULA

For n>=3, a(n)=A000096(n-2).

From Chai Wah Wu, Oct 12 2018: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 5.

G.f.: x^2*(3*x^3 - 8*x^2 + 6*x - 2)/(x - 1)^3. (End)

EXAMPLE

a(1)=0 because (1(3-1)/2) mod (1(1+1)/2) = 1 mod 1 = 0,

a(2)=2 because (2(6-1)/2) mod (2(2+1)/2) = 5 mod 3 = 2.

MATHEMATICA

Table[Mod[n(3n-1)/2, n(n+1)/2], {n, 1, 120}]

CROSSREFS

Cf. A000096 n(n+3)/2, A000217 Triangular numbers n(n+1)/2, A000326 Pentagonal numbers:n(3n-1)/2, A175630 a(n) = n-th pentagonal number mod (n+2)., see also A080956, A132315-7.

Sequence in context: A024308 A059432 A256488 * A243816 A243159 A258144

Adjacent sequences:  A175628 A175629 A175630 * A175632 A175633 A175634

KEYWORD

nonn

AUTHOR

Zak Seidov, Jul 29 2010

STATUS

approved

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Last modified September 18 07:39 EDT 2020. Contains 337166 sequences. (Running on oeis4.)