OEIS A000217 - Implementation in D

Triangular numbers: a(n) = binomial(n+1,2) = n*(n+1)/2 = 0 + 1 + 2 + ... + n.

a(n) = 2*a(n-1)-a(n-2)+1, where a(0) = 0 and a(1) = 1

Source code

Recurrence with function in string form...

import std.stdio, std.range;

void main() {
    auto a000217 = recurrence!("-a[n-2]+2*a[n-1]+1")(0, 1);
    // auto a000217 = recurrence!"a[n-3]-3*a[n-2]+3*a[n-1]"(0, 1, 3);
    
    a000217.take(54).writeln;
}

Output

[0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666, 703, 741, 780, 820, 861, 903, 946, 990, 1035, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1431]