A272058 Start with all terms set to 0. Then add n to the next n+3 terms for n=0,1,2,... .

0, 0, 1, 3, 6, 10, 14, 20, 25, 33, 39, 49, 56, 68, 76, 90, 99, 115, 125, 143, 154, 174, 186, 208, 221, 245, 259, 285, 300, 328, 344, 374, 391, 423, 441, 475, 494, 530, 550, 588, 609, 649, 671, 713, 736, 780, 804, 850, 875, 923, 949, 999, 1026, 1078, 1106

Offset: 0

Author

Wesley Ivan Hurt, Apr 19 2016

Keywords

• nonn
• easy

Examples

			n  | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,10, ...
__________________________________________
     0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...
+       0, 0, 0
+          1, 1, 1, 1,
+             2, 2, 2, 2, 2
+                3, 3, 3, 3, 3, 3
+                   4, 4, 4, 4, 4, 4, 4
+                      5, 5, 5, 5, 5, 5, 5, 5
+                         6, 6, 6, 6, 6, 6, 6, 6, 6
+                            7, 7, 7, 7, 7, 7, 7, 7, 7, 7
+                               8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
+                                  9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9
+                                     ...
__________________________________________
a(n)|0, 0, 1, 3, 6,10,14,20,25,33,39, ...
		

Links

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

Crossrefs

Cf. A095794, A258087.

Programs

Magma

[0,0] cat [(6*n^2+6*n-23+(7-2*n)*(-1)^n)/16 : n in [2..100]];

Maple

A272058:=n->(6*n^2+6*n-23+(7-2*n)*(-1)^n)/16: 0,0,seq(A272058(n),n=2..100);

Mathematica

CoefficientList[Series[x^2*(1 + 2 x + x^2 - x^4)/((1 - x)^3*(1 + x)^2), {x, 0, 50}], x] (* or *)
LinearRecurrence[{1, 2, -2, -1, 1, 0, 0}, {0, 0, 1, 3, 6, 10, 14}, 60]

Formula

G.f.: x^2*(1 + 2*x + x^2 - x^4)/((1 - x)^3*(1 + x)^2).

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n > 6.

a(n) = (6*n^2 + 6*n - 23 + (7 - 2*n)*(-1)^n)/16 for n > 1.

a(n) = floor((n+3)/4) * floor((3*n-4)/2) + (floor((n-1)/2) mod 2) * floor((3*n-3)/4) for n > 1.

For n > 1, a(2n) = A095794(n). - Jon E. Schoenfield, Feb 19 2022