A076307 a(n) = n+min(2*floor(a(n-1)/2), 3*floor(a(n-1)/3)) for n > 1, a(1)=1.

1, 2, 3, 6, 11, 15, 21, 28, 36, 46, 56, 66, 79, 92, 105, 120, 137, 153, 171, 190, 210, 232, 254, 276, 301, 326, 351, 378, 407, 435, 465, 496, 528, 562, 596, 630, 667, 704, 741, 780, 821, 861, 903, 946, 990, 1036, 1082, 1128, 1177, 1226, 1275, 1326, 1379, 1431

Offset

1,2

Links

Table of n, a(n) for n=1..54.

Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1).

Formula

a(n) = n*(n-1)/2 + b(n) where b repeats the period (1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0) of length 12.

a(n) = +2*a(n-1) -a(n-2) +a(n-12) -2*a(n-13) +a(n-14).

G.f.: -x*(1+2*x^4-x^5+2*x^6+x^7+x^8+2*x^9+2*x^12+2*x^3) / ( (1+x) *(1+x^2) *(1+x+x^2) *(x^2-x+1) *(x^4-x^2+1) *(x-1)^3 ).

Mathematica

LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1}, {1, 2, 3, 6, 11, 15, 21, 28, 36, 46, 56, 66, 79, 92}, 60] (* Harvey P. Dale, Nov 29 2013 *)

Prog

(Magma) [ n eq 1 select 1 else n+Min(2*Floor(Self(n-1)/2), 3*Floor(Self(n-1)/3)) : n in [1..60] ]; // Klaus Brockhaus, Dec 03 2010
(Magma) b:=func< n | [1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0][(n mod 12)+1] >; [ n*(n-1)/2+b(n-1): n in [1..60] ]; // Klaus Brockhaus, Dec 03 2010

Crossrefs

Sequence in context: A090304 A005211 A298702 * A102990 A351203 A138519

Adjacent sequences: A076304 A076305 A076306 * A076308 A076309 A076310

Keyword

easy,nonn

Author

Benoit Cloitre, Nov 06 2002

Status

approved